Party leaders said that Mr. Norton appeared to be a straw candidate for Democrats, one intended to help Representative Ruben Gallego, the likely Democratic nominee for the open Senate seat. The leaders also said that they viewed Mr. Hernandez as a proxy for Republicans and that party’s leading Senate candidate, Kari Lake, an ally of former President Donald J. Trump who refused to accept the results of both the 2020 election and her defeat in the governor’s race in 2022.

Party officials said they were concerned that Mr. Norton might drop out of the race if he won the primary, making it less likely that a minor-party candidate would siphon votes from Mr. Gallego. The thinking of party leaders is that Mr. Hernandez would stay in the race if he won the nomination, running interference for Ms. Lake.

The Green Party has endorsed Eduardo Heredia-Quintana, the chair of the Green Party of Pima County, urging its members to write in his name on their primary ballots.

“They’re not even trying to cover their tracks at this point,” Cody Hannah, a co-chair of the Arizona Green Party, said in an interview on Friday. “We know these people aren’t members of our party. We know they aren’t genuine Greens.”

Efforts to reach Mr. Norton and Mr. Hernandez were not immediately successful.

Neither Arizona’s Democratic Party nor its Republican Party responded to requests for comment on Friday. The campaigns for Mr. Gallego and Ms. Lake also did not provide comment.

Democrats narrowly control the Senate, an advantage that could hinge on Arizona’s contest in November, which the nonpartisan Cook Political Report considers a tossup.

The seat is being vacated by Senator Kyrsten Sinema, who left the Democratic Party to become an independent before announcing in March that she would not seek re-election.

The jockeying over the Green Party’s ballot line is a microcosm of the larger scrutiny of third parties in the 2024 election, along with independent candidates, including Robert F. Kennedy Jr., who is running for president.

In several instances this election cycle, Republicans have tried to prop up minor-party candidates to lure disaffected progressives and antiwar voters away from the Democratic Party, while Democrats have sought to make it more difficult for them to gain access to the ballot amid consternation that they could play the role of spoilers for the party.

Green Party leaders said Mr. Norton had raised more than $30,000 from super PACs and prolific donors aligned with the Democratic Party, which was consistent with a New York Times review of Mr. Norton’s campaign receipts. Two of the super PACs have publicly endorsed Mr. Gallego.

Neither of the super PACs responded to a request for comment.

Mr. Hernandez drew scrutiny from the Green Party when a Republican lawyer recently represented him in a court case — brought by Democratic-aligned plaintiffs — challenging his eligibility as a candidate and whether his petition circulators had complied with the law. A judge ruled that Mr. Hernandez should be included on the ballot.

A treasurer listed by Mr. Hernandez on campaign filings with the Federal Election Commission was named last year as a board member of a “dark-money” nonprofit created by Nevada’s governor, Joe Lombardo, a Republican, which he used to attack Democrats.

Mr. Hannah, the Green Party’s co-chair, said party members were not familiar with either Mr. Hernandez or Mr. Norton.

“We know the faces who show up at our meetings,” he said. “We know the people who volunteer. It definitely made us suspicious, if nothing else.”

While only Green Party members can vote in its primary, independent voters are eligible to sign the petitions of candidates seeking access to the party’s ballot line, Mr. Hannah said. Mr. Norton and Mr. Hernandez needed at least 1,300 names each, and, according to Mr. Hannah, most of the signatures collected by them had not come from Green Party members.

“These are people who essentially have no connection to our party deciding who’s on our primary ballot,” he said.